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Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?

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If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?

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A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

Heavy Hydrocarbons

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Remember that molecules with more than one hydrogen and carbon atom can have isotopes at different places. For example, in ethane, a carbon-13 could occur at either of the carbon sites!